Hydrogen reacts with Oxygen to form water. You can calculate how much heat is released, you can find the heat of reaction from internet or any chemistry textbooks. After burning, the amount of each species, the temperature, and volume of the system will change. The amount of change, you can calculate using the stoichiometry of the reaction. Once you have the mole fraction of each species (H2, O2, N2,H2O,etc.), you find the heat capacity of each species from some reference, and the heat capacity of the mixture would be the sum of mole fraction multiplied heat capacity. The temperate change would be the released heat divided by the mixture heat capacity. You can use the ideal gas law to find the partial pressure of O2.
The flame temperature you can get from Figure 1 of the following paper.
Article HYDROGEN USE IN INTERNAL COMBUSTION ENGINE: A REVIEW